Implications of molecular orbital symmetries and energies for the electron delocalization of inorganic clusters.

Isostructural clusters exhibit contrasting magnetic properties when the number of electrons differs. Surprisingly, the same is true even for isoelectronic cages (e.g. O(h) B6H6(2-) is diatropic, whereas O(h) Si6(2-) is paratropic) or for those with different substitutents (e.g. T(d) B4H4 is paratropic, whereas T(d) B4F4 is diatropic). Indeed, the total nucleus-independent chemical shift (NICS) values, based on shieldings computed at cluster centers, may range considerably in magnitude and even change from diatropic (up-field shifted) to paratropic (down-field shifted). Similarly, individual dissected canonical molecular orbital contributions to the total NICS values computed at the "gauge-including atomic orbitals" (GIAO) level vary greatly. This contrasting behavior arises from molecular orbital energy differences, from the extent of orbital overlap, as well as from symmetry-based selection rules derived from group theory. Differences in magnetic properties may originate from the symmetry of the orbitals; specifically from the forbidden nature of the highest occupied molecular orbital --> lowest unoccupied molecular orbital (HOMO --> LUMO) electronic excitation weighted by the occupied-unoccupied orbital energy difference. Thus, HOMO-NICS values are generally highly paratropic if the HOMO --> LUMO rotational transition is allowed by symmetry selection rules.